Certified Reduced Basis Method for Electromagnetic Scattering and Radar Cross Section Estimation

Yanlai Chen (1) , Jan S. Hesthaven (2) , Yvon Maday (2, 3) , Jerónimo Rodríguez (4) , Xueyu Zhu (2)

1 umassd - Department of Mathematics
2 DAM - Division of Applied Mathematics
3 LJLL - Laboratoire Jacques-Louis Lions
4 Departamento de Matemática Aplicada

We study nontrivial applications of the reduced basis method (RBM) for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section (RCS). The method and several extensions are explained with two examples with different characteristics. Parameters that are allowed to vary within the model include frequency, incident angle and measurement angle as well as the geometry of the scatterers. With appropriate applications of the empirical interpolation method (EIM), transformation of the domain, configuration of perfectly matched layer, exponential convergence of the reduced basis solution over the entire parameter domain is achieved. Moreover, we demonstrate that this approach allows for the effective capture of the critical behavior, in this case through shapes that minimize scattering. This further highlights the robustness and quality of the greedy approximation and the reduced basis method approach.

Mots clés: Reduced Basis Method; Electromagnetic Scattering; Radar Cross Section; Empirical Interpolation Method

Domaines: Analyse numérique [cs.NA]

Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jerónimo Rodríguez, Xueyu Zhu. Certified Reduced Basis Method for Electromagnetic Scattering and Radar Cross Section Estimation. 2011. ⟨hal-00644805⟩